Core Structures in Random Graphs and Hypergraphs
| dc.comment.hidden | The results in one of the chapters in my thesis are based on a paper published in a journal (Random Structures and Algorithms). One clause in the copyright agreement allows the re-use of the material under certain circumstances. I consulted Trevor Clews (GSO) and Christine Jewell (Library) and both agreed that use in the thesis complies with the terms. | en |
| dc.contributor.author | Sato, Cristiane Maria | |
| dc.date.accessioned | 2013-08-30T15:21:48Z | |
| dc.date.available | 2013-08-30T15:21:48Z | |
| dc.date.issued | 2013-08-30T15:21:48Z | |
| dc.date.submitted | 2013 | |
| dc.description.abstract | The k-core of a graph is its maximal subgraph with minimum degree at least k. The study of k-cores in random graphs was initiated by Bollobás in 1984 in connection to k-connected subgraphs of random graphs. Subsequently, k-cores and their properties have been extensively investigated in random graphs and hypergraphs, with the determination of the threshold for the emergence of a giant k-core, due to Pittel, Spencer and Wormald, as one of the most prominent results. In this thesis, we obtain an asymptotic formula for the number of 2-connected graphs, as well as 2-edge-connected graphs, with given number of vertices and edges in the sparse range by exploiting properties of random 2-cores. Our results essentially cover the whole range for which asymptotic formulae were not described before. This is joint work with G. Kemkes and N. Wormald. By defining and analysing a core-type structure for uniform hypergraphs, we obtain an asymptotic formula for the number of connected 3-uniform hypergraphs with given number of vertices and edges in a sparse range. This is joint work with N. Wormald. We also examine robustness aspects of k-cores of random graphs. More specifically, we investigate the effect that the deletion of a random edge has in the k-core as follows: we delete a random edge from the k-core, obtain the k-core of the resulting graph, and compare its order with the original k-core. For this investigation we obtain results for the giant k-core for Erdős-Rényi random graphs as well as for random graphs with minimum degree at least k and given number of vertices and edges. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/7787 | |
| dc.language.iso | en | en |
| dc.pending | false | en |
| dc.publisher | University of Waterloo | en |
| dc.subject | combinatorics | en |
| dc.subject | graph theory | en |
| dc.subject | random graphs | en |
| dc.subject | probabilistic | en |
| dc.subject | enumeration | en |
| dc.subject.program | Combinatorics and Optimization | en |
| dc.title | Core Structures in Random Graphs and Hypergraphs | en |
| dc.type | Doctoral Thesis | en |
| uws-etd.degree | Doctor of Philosophy | en |
| uws-etd.degree.department | Combinatorics and Optimization | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |